The ultimate sensitivity performances obtained with a continuous wave-cavity ring down spectroscopy setup in the near infrared are investigated. At fixed frequency, the noise of the photodetector is found to be the main limitation and the best limit of detection (about 10-11 cm-1) is reached after a 10 s averaging. We show that long term baseline fluctuations can be efficiently averaged over several days allowing us to reach a detection limit as low as 5 × 10-13 cm-1. The achieved sensitivity is illustrated on narrow spectral intervals where the weakest lines detected so far by absorption spectroscopy are observed: (i) ultra-weak transitions of the a1Δg(0)-X 3Σg-(1) hot band of 16O2 near 1.58 μm and (ii) first detection of an electric quadrupole transition in the second overtone band of nitrogen (14N2) near 1.44 μm.